Multiple mode closed-cycle control system



1953 D. c. MCDONALD 5f AL 2,663,832

MULTIPLE MODE CLOSED-CYCLE CONTROL SYSTEM Filed Oct 1, 1952 4 Sheets-Sheet 1 1N VEN T 0R5.

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1953 D. c. MCDONALD ET AL 2,663,832

MULTIPLE MODE CLOSED-CYCLE CONTROL SYSTEM Filed Oct. 1, 1952 4 Sheets-Sheet 2 4'9 if Q fi 60 2 3 45 .6O\ 52 5/ T If,

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TORQUE ON-QFF DIRECTIONAL VJ CONTROL CCINTROL 39 272; 7 & '32 %34 LEAD L nc I W B T NETWORK AMPLIFIER MODULW ,qMPL/F/ER 3 Home INVENTORS.

Dec. 22, 1953 D. c. M DONALD ETAL 2,663,832

MULTIPLE MODE CLOSED-CYCLE CONTROL SYSTEM Filed Oct. 1, 1952 4 Sheets-Sheet 3 o'Lt ,2/0 207 200 03 I ZZ 206 AMPLIFIER IN VEN T 0R5. (f/ffroaml .6 W M644. (3 ham Dec. 22, 1953 D. C. MDONALD ET AL MULTIPLE MODE CLOSED-CYCLE CONTROL SYSTEM 4 Sheets-Sheet 4 Filed Oct. 1, 1952 mww MWN

?atented Dec. 22, 1953 MULTIPLE MODE CLOSED-CYCLE CONTROL SYSTEM Donald C. McDonald, Skokie, Kenneth C. Mathews, Evanston, and Robert 0. Bee, Des llaines, 111., assignors to Cook Electric Company, Chicago, 111., a corporation of Illinois application October 1, 1952, Serial No. 312,482

14 Claims.

This invention relates to improvements in closed-cycle control systems, and, more particularly, to closed-cycle control systems wherein positional agreement is desired between a controllable input element and an output element whose position is to be controlled correspondnsly.

It is the principal object of this invention to provide improved methods and apparatus for operating such closed-cycle control systems.

It is a further object of this invention to provide improved apparatus for such closed-cycle control systems wherein optimum positional agreement will be maintained at all times for devices having limited power or velocity charac teristics.

It is often desired to control the position of a mass having large inertia without actually having the control apparatus supply the energy necessary to move the mass and overcome said inertia. An excellent example this type of operation is in a gun director or the like wherein an operator or automatic tracking device i01- IOWS a target in a determinable pattern and it is desired that a gun and mount of great mass will automatically follow the same pattern. It is obvious that manpower or a delicate automatic tracking device cannot supply the energy necessary to move such a mass with speed and accuracy. They can, however, generate a signal characteristic of such pattern which can control an extrinsic power source to drive such a mass.

Many attempts have been made to create device which will adequately accomplish a fulfillment of broad aim but all have failed to provide a totally satisfactory solution. All closed.- cycle controllers presently known can be classed in one of two general categories. The first class utilizes an on-off or contactor mode of operation wherein a device compares the relative positions of a controlling element and a controlled element, and when there is a positional difference of a predetermined magnitude between these elements a switch is closed which will apply the maximum force of a motive means to the con trolled element to bring said element into substantial positional agreement with the controlling element. This type of system has the obvious disadvantage of erratic, inaccurate motion, as a certain predetermined error is necessary bofore the motive power is applied, and when the power is applied the maximum power of the device is always used. It has the advantage of very rapid response and minimum time of reducing an error to zero, but it has the accompanying disadvantage of applying the maximum force of the energy source with resultant oscillations overshoot of the zero position.

The second general class into which the prior known devices fall is a class of devices having continuous control of an output. in these de vices a force is applied as a linear function of the relative position, velocity, or other variable of the controlled element with respect to the controlling element. These devices can be c2esigned to position the controlled element rel tively accurately with respect to the contrc'" element when the relationships of said elerne are relatively constant over a long period of tin e. Such linear devices having the controlling ment in steady state operation can be designed to have a zero positional difference between the controlling and controlled elements, but su h a linear device is characterized by poor response to rapid changes in the relationship of the controlling element or input to the controlled element or output. This slow response is a result of two factors detrimental to controller speed. The controlling signal is proportional to the positional difference or rate-of-change oi positional difierence of the two elements, and thus small differences produce small signals and consequent small correcting forces. Additionally, while the ideal controller would positively accelerate idly to a predetermined point and then rap lv decelerate to both positional and velocity agi ement with the controlling element, these linear devices undergo a gradual acceleration, torque reversal, and deceleration ith consequent increase of response time and loss of tracking.

Thus, all or" the systems heretofore known have evidenced one or more of the following ta ts- They will either be sluggish in response to 1 changes in position or velocity and be extre'r large with large power control apparatus in case of linear devices, or, they will be inaccurate, tending to oscillate or hunt and overshoot of the type of device known as contactor con Therefore, it is an additional object of s invention to provide a control device which w I operate as a linear control for very small p =itional diiierences or rate-oi-chan e of position difierences, but will act as a contactor control for larger positional differences or rate-of-change oi position differences.

It is an additional object of this invention to reduce the weight, power requirement, and t of control devices by eliminating the need linear controls and amplifiers which would. 0-; capable of the power necessary to provide the re quirement for large positional differences in linear operation.

It is a further object of the invention to ac complish the advantages of increased speed and accuracy by operation in multiple modes wherein the mode of operation is to be determined by a function of the positional difference and the rate-of-change of the positional difference of the device.

Additional objects of the invention will become manifest from the description, accompanying drawings, and appended claims.

In carrjing out this invention in one form, a closed-cycle control system is provided which will control the angular position of a rotating shaft in response to the angular position or" a controlling shaft. Thi type of control is generally termed a servo mechanism and shall hereinafter be referred to as a servo. More particularly one form or" the invention consists of a motor and a load, a controlling shaft or input source, a means for comparing the position of the load and the input source to generate an error voltage proportional to positional difierence, an essen ially linear amplifier for such an error voltage,

an electronic computer to derive a voltage which is a function of such an error and the rate-ofchange of such an error, and a control actuated by the output of the computeto apply the out put of such an amplifier to the motor in order to drive the load when the input and load are in substantial positional agreement, and to apply a maximum voltage to the motor in order to drive the load. toward positional and velocity agreement with maximum torque when the error and error-rate function increases beyond a predeter mined magnitude as determined by the electronic computer and associated control.

For a more complete understanding or this invention, reference should now be made to the drawings, wherein:

Figure 1 illustrates a phase-plane diagram of a servo employing the teaching of this invention;

Fig. 2 is a response time plot of various modes of operation for a step input error;

Fi 8 is a block diagram of such a servo;

Fig. l is a sch matic circuit diagram of computer elements of the servo of Fig. 3;

Fig. 5 is a schematic circuit diagram of biased diode squaring circuit of Fig. 3;

Fig. 6 is a curve representing the input-output characteristics of such a diode circuit;

Fig. 7 is a block diagram of a second embodiment employing the teaching of this invention; and

Fig. 8 is a schematic circuit diagram of the computer portions of the apparatus shown in Fig. 7.

fieferring now to the drawings, and more particularly to Fig. l, a phase plane diagram is illustrated which depicts the general characteristics or a typical servo operating in two modes in accordance with this invention. The abscissa of this diagram represents the error E, or positional diiference between an angular input A1, and an output A0. The ordinate of the diagram 1'ep1-e sents the error rate 1 or the rate-of-change of relative position of the input and output shafts of such a servo. This phase-plan diagram is a valid means of representation of the characteristics of any single-degree-of-freedom control system. In such a diagram, time is eliminated from the usual velocity and position equations and a single plot of velocity and position is used. From this diagram the characteristics of a servothe the

mechanism can be analyzed to clearly illustrate its response time, maximum error, and other characteristics of a given device having some limited maximum torque and a predetermined moment of inertia.

A contactor or ofi-on servo has the characteristic equation of motion:

(1) JE=-TE 0 and 10 Jii=-TE c where J is the combined moment of inertia of the servo motor and load, is the acceleration of the error, and T is the full torque oi": the servomotor.

This equation sets out that for any positive error, negative torque is applied and. for negative error, positive torque is applied to the load in an attempt to reduce the error to zero. If a contactor servo is analyzed by this system, it can be seen that if a positive error or" any arbitrary magnitude is introduced between the input and output shafts, the motive means will apply a negative torque to the output shaft which will drive the output shaft to eliminate the error. This is illustrated in Fig. 1 as an error, indicated. on the curve at ii, which indicates a step function difference or? position between an input and output shaft. From the above equation, this applies the torque of a driving means which will tend to negatively accelerate the output with respect to the input, and thus a phase-plane curve of such a device will follow the curve 22 in Fig. l in the direction indicated by the arrows. As the load decelerates, that is, E becomes more negative, the positive error will be reduced toward positional agreement. The driving means would be thus energized until the curve reaches the point on the ordinate indicated as 53, at which time the error, or value of the abscissa, is zero. However, the additional torque or kinetic energy having been introduced into the device, the output shaft will continue at its new velocity and immediately create a negative error, thus applying positive torque to the load from the motor. The load will be accelerated by the full torc'ue of the motor and will follow curve i i until the error E is again reduced to zero at its at which point negative torque will once again be applied and cause the load to follow curve 5 5. Thus, the phase-plane curve will follow curves i2, M and it in a stable oscillatory motion, whereby the device will have positive and negative torques alternately applied to it as the error changes from negative to positive values respectively.

It can be seen that thecurves 52, i l and i are substantially parabolic in character as the torques and consequent accelerations F1 are constant and thus, from the calculus, the error E and error-rate E will have a substantially para= bolic relationship. It should be further noted that irrespective of the magnitude of the ste function that might be used, such a device will always have a phase-plane portrait of this general character and shape. The magnitude of the respective intercepts or the E. and It axes will be determined by the physical structure, namely, the ratio or the maximum torque of the motor and the inertia of the system.

In a linear servo mechanism, a correcting torque is applied to the output or load as a func-- tion of error and error-=rate, according to the fo1- lowing general equation derived from'the familiar or motion equation:

Where Z: rror rate coefficient and K: steady state gain of the servo amplifier. Thus, unless the error or error-rate Or a combined function of these factors is equal to or exceeds the maximum for which the device is designed, the maximum torque of the device will never be applied to the load. This necessarily-means that correct n oi input error will not be efiected in the to churn possible time as in the full torque operation, but will be corrected over a longer period of but with a resulting reduction of the oscillatory motion characteristic of axcontactor type or" serve. This type or" linear control is illustrated in g. l by the curve ll where 9. -tion or error rate E is introduced into can be seen that for a given error:-

than that applied by a contactcr type of c ntrol and will thus result in a phaselane portrait having asmaller slope at any given point on the curve. The slope of such a phase-plane portrait is proportional to E is low which is a function of error and erroruate, as shown in Equations 2 above, will have a negative component corresponding to the positive error and a compensating positive component oorre -educed to zero. As the portrait passes bethe abscissa, the torque applied to the output,

spending to the negative error-rate. The magnitude of this error-rate damping will be determined by the relative magnitude of the constants 7c and Z, and the inertia of the system.

This relationship of 7c and Z will determine the response time of the system and the stability and freedom from hunting of the control. This stable positional agreement is an extremely desirable characteristic where the intended use reuuires that the input and output be in substantial positional agreement during operation with changes of At or A1 or when operating in a steady state condition. The curve 53 indicates the same linear servo operating with a small r input step function of error-rate showing that the general shape and character of the curve are unchanged for changes in magnitude of the input step function.

While the system described here uses only error-rate damping, it should be sent in that the principles of this invention are equally applicable to any type of linear control having viscous or coulomb output damping, integral control, or any control function or" either input position, output position, error or any integrals or derivatives thereof.

It can be seen from this diagram that it would be desirable to operate a servo mechanism in the linear mode for small errors or error-rates, but to be able to the maximum torque of the drive motor when the error or error-rate increases to some predetermined magnitude. Such a servo will apply the niaximumtorque for all error and error-rate functions larger than a predetermined.

magnitude to give the maximum possible accele- 6 rations, but for. small functions of error and error-rate, the servo operates in the linear mode withsubstantial damping and integral control to accurately follow the input as desired.

To create a device with the optimum response, the controls should function to reduce the error E and error-rate E to zero concurrently. The obvious fault of the contactor type of device is that itreduces only one of these factors to zero in any given quadrant of its phase-plane portrait. In accordance with this invention, instead of causing torque reversal at point I 3 on the ordihate, the computing mechanism eifects a torque reversal at point 2! which is found by constructing parabola 22 of the same shape as curve H but with its center at the origin. Thus by effecting torque reversal at point 2|, the phase-plane portrait of a servo built in accordance with this in-- vention will follow curve 22 to the origin in the minimum possible time for a device having torque limitations. origin, operation reverts to the linear mode by any convenient switching means. If such a servo is additionally limited by velocity saturation, that is, if the input velocity in approaches the maximum speed of the motive means, i. e., approximately 1750 R. P. M. for a 4 pole, 60 cycle induction motor, then negative error-rates can only be utilized up to the point Where Ai+E'=the maximum speed of the motor. This is illustrated in the phase-plane portrait as line 26 which is a constant velocity mode line, and the line along which such a servo will operate when at velocity saturation. The teaching of this invention is equally applicable to a device operating in the velocity saturation mode. Thus, in Fig. 1, in accordance with this invention, the servo follows curve I? from the input step function on the ordinate to the point I9 as a linear servo mechanism and then follows the curve I 2 as a contactor type of servo, with maximum torque, to point 2| where the torque is reversed and the device follows torque reversal curve 22 to to the area of the origin Where it once again switches to the linear mode. Thus the advantages of linear operation for small errors and contactor operation for large errors are combined to achieve the optimum in servo performance.

In Fig. 2, curve 23 illustrates diagrammatically the time response of a servo having very little damping and this would be substantially the curve or a contactor type of control. It can be seen, as, time increases to the right, in Fig. 2, the error of such a device is rapidly reduced to zero, but thence continues to oscillate about the axis. The, curve 24 is for a critically damped linear control, and this curve approaches zero error Very slowly but doesnt oscillate or hunt as does the underdamped device. A device constructed in accordance with this invention will operate along curve 25 which is substantially coincident with curve 23 until the error is reduced to a predetermined value, at which time the torque is reversed to prevent the overrun characteristic of contactor operation. As the system approaches zero error, it reverts to linear mode operation to fol low a curve similar to the latter portion of curve 24.

A device for accomplishing this is illustrated in the block diagram of Fig. 3. Rotating input shaft 3| is a driving means for the continuously rotatable wiper of potentiometer 30. A source of potential 32 is connected across this potentiometerand in parallel with a second potentiometer 33 which is driven by the output shaft 35 driving As curve 22 approaches the 7 the servo load 3 Thus when the output shaft 35 is in positional agreement with the input shaft 3!, the voltage present on wiper 36 will be zero with respect to ground. However, if the output shaft has a position difierent from that of the input shaft, a voltage will be present at wiper 36 which will be positive or negative, depending upon the relative position of the two shafts. This output voltage will be fed into a lead network 3'5 which is capable of generating a voltage proportional to positional difference or error and the rate-of-change of said error. Such lead networks are well known in the servo art. The output of lead network Si is then fed through conductor 3% to a D. C. amplifier as and through a normally closed switch it to a modulator M. The modulator may be of any well-known type whereby a 0. signal is applied to the grid of an electron tube to modulate an A. C. signal present upon the plate of said tube. Thi modulated A. C. signal is then fed through conductor 2 to an A. C. amplifier 3 and thence to an A. C. motor t l which may he of any conventional type, but is here shown as a two-phase induction motor having controlled winding, and winding it in series with shifting con-denser ll. Coil i5 is energized by the controlled output of amplifier :33. The output of this motor then drives the load 3% and keeps load t l in positional agreement with input 34 by the amplified signal from the potentiometer. This is a most satisfactory mode of operation of a servo for any small variations of error or error-rate. However, it is desirable when a function or" the error or error-rate reaches a predetermined magnitude to apply the maximum signal to the modulator ll necessary to produce the maximum torque from the motor The computer section 58 or this servo system is used to compute and generate a voltage which will be proportional to a function of the error and errorrate and will control the application of full torque to motor M. The output of potentiometer 33 is fed to circuit it which applies a constant multiplier l; to generate a new voltage equal to In parallel with circuit 59 is a circuit as de signed to take the derivative of the error to produce at its output a voltage proportional to the error-rate 13. This error-rate voltage is fed to the circuit ll through conductor 52 which will produce a voltage proportional to the square of said error-rate E and at the same time retain the sign of the error-rate, e., The output of circuit El and the output of circuit :39 are then applied to sumr-iation circuit be which will arithmetically combine the two voltages to produce a voltage proportional to the square of the error-rate and the error, i. e., KE+E]E'\=C1. The output of the summation circuit is connected by conductor to an electronic switch 5-3. This electronic switch will normally have a voltage present upon it so that it will normally be in an actuated condition. However, when the voltage of the summation circuit C1 goes to zero-in other words, when the value of Kit is equal to the value of but of opposite sign--the electronic switch will he ole-energized. This point is the desired point of torque reversal of the driving means, represented by all points on curve 22 in l, and the electronic switch will affect this torque reversal by changing the D. C. output voltage from a positive to a negative character with a consequent phase inversion of the input to coil t5. Thus the computer portion synthesizes a voltage proportional to ElEH-KE from the output of potentiometer t3 and this voltage will determine the line of torque reversal 22 which will coincide with the path of the phase-plane portrait to the origin at full negative torque. While this computer output is the function for minimum correcting time, other functions can be chosen for various control characteri tics without depart ing from this invention.

The output of circuit 49 is also fed to a second circuit 55 which will act to convert the output of circuit 59 into a voltage of absolute magnitude lKEl. In other words, if the error voltage be positive or negative, the output of circuit 55 will always be of the same sign, 1. e., negative. In a like manner, the output of circuit Si is connected to a circuit 55 which will generate a voltage proportional to the absolute value of the output voltage of the circuit 5|. The outputs of 55 and 55 are then combined in a summation circuit ill which will produce a voltage equal to the sum or" the absolute values of the outputs of circuits and 5! [E |+|KE|=Cz. The output of thissummation circuit 5'5 is connected by conductor 5% to a second electronic switch 59 which will determine the control of switch so. The position of switch ill normally applies the linear control to modulator ll. When the sum of the absolute magnitudes, C2, exceeds a predetermined magnitude represented by the curves 52, i l and in Fig. 1, the on-ofi" control 5% will move switch to the actuated position. At this time, the torque directional control 513 will apply a D. C. voltage to the modulator ii of a magnitude which will produce output torque and or a correct to produce the torque in the direction re quired to reduce the error to zero. The operation of computer circuit is can better be understood from Fig. 4 which is a schematic cn'cuit diagram of the elements indicated by blocks 59, iii, 55, 55, El and til. In Fig. 4, the error voltage is applied between terminals and ground. A portion of this voltage E is tapped off by potentiometer tit and supplied to the grid of tube 8? which is one tube of a series D. C. amplifitr, including tubes 6? and 68. The series I). C. amplifier uses two triodes in a common envelope, one as the amplifier, and the second as a constant load for the amplifier. Thus, for any changes in filament voltage or changes within the tube fro l aging, substantially no change will be evident the output of the amplifier circuit. Resistor is a cathode bias resistor for the amplifier, and resistor ii is the cathode bias resistor for the load triode 68. The output of this amplifier is "pplied to a cathode follower circuit through tor F2. The cathode follower consists of a bi ode 13, load resistors it, it, and potentioniet "it. A portion of the voltage present across t load resistors controlled by potentiometer l5 present across potentiometer Ti and is there applied to a clifierentiating circuit. The differen tiating circuit is represented by condenser is and resistor '59. The relative magnitudes of these elements it and 19 are so chosen as to produce a voltage at their output across potentiometer i which is substantially the time derivative of the voltage present across potentiometer ll. The wiper of potentiometer Si then applies a voltage to the triode 82 which is again in a series B. amplifier circuit consisting of triooles 82 and as within the same envelope, cathode bias resistor 84 for the load tube 83, and cathode bias resistor 85 for the amplifying tube 22. The output of this D. C. amplifier is taken from the plate of tube 32 and applied to a cathode follower triode 816 through a grid resistor 90. The load of cathode follower 85 consists of resistors 81 and 83 and a potentiometer 89. The voltage present on the Wiper of potentiometer 89 is proportional to the error-rate. This signal is applied to a squaring circuit SI which will be described hereinafter. This squaring circuit produces at its output a volta e canal to EIEI. The outp t the squaring circuit 95 is then applied to resistors 92 and 93 which are arranged as a voltage divider.

Wiper 94 of potentiometer TI is adjusted to tap ofi a portion of the voltage across potentiometer I'I, proportional to KE, and apply it through conductors 95 and 95 and resistor 31 to resistor 93 which forms a common summing circuit for the output or the squaring circuit, which is proportional to FIE}, and the voltage from wiper 94, which is proportional to KE. This output is then applied through conductor 98 to the torque direction control es of Fig. 3, as described above.

The signal present at wiper 94 is also connected through conductor 95 and conductor 99 to potentiometer IQI and back to ground through conductor I62. The wiper I03 of potentiometer IIBI is adjusted to apply a fixed proportion of the voltage to the grid of tube I04. Tubes IM and I are connected with a common cathode resistor I65 through potentiometer I9! to form a differential amplifier circuit. This circuit functions broadly as follows: A signal is applied to the grid of tube I 04 causing a change in current through the circuit including cathode resistor Hi6, a portion of potentiometer IIl'I, tube I04, and its load resistor I28. This change in current in resistor I86 causes a change in the cathode bias which is normally present on tube I135. This causes a resulting change in conduction of the circuit including cathode resistor I26, tube I95, and its load resistor I09, and for increases in the current through tube IE4 there will be a resulting decrease in the current through tube I85. Thus, the voltage applied to tube II I, which is the output of tube I 04, will be 180 out of phase with the signal which is applied to the grid of tube I i2, which is the output of tube I05. Tubes III and H2 are connected in cathode follower circuits. Tube II2 has cathode resistors H3 and H4, and tube III, cathode resistors H5 and IIS associated therewith. Res stors II 4 and I I6 are connected across balancing potentiometer Ii! and a common cathode resistor I I8, which is connected through conductor IIQ to termina 520 which carries a negative voltage of the order of. 150 volts. The output of the cathode follower tube H2 is applied through a rectifier 425 to resistors 22, I25 and I2! and thence by conductor I23 to ground. Rectifier I2! is so oriented in the circuit that it will conduct when the junction between resistors I I3 and I I4 is negative with re spect to ground, thus producing a negative output voltage across resistor I27. This will be when the signal present at potentiometer w; :1 which represents KE. is also negative with respect to ground. The cathode follower of tube HI is connected to a rectifier I2 3 through a re sister I 25 and resistor I 26 to common load resistor 92? for the outputs of tubes HI R tifier 524 is also oriented so that a negative 'llcl e win cause current to how through resistors lEE. I28 I 27, and conductor I 23 to ground. This will be true when the voltage on the grid of tube I l i is negative, which will be the case only when the signal present at wiper I63 is positive and,

10 consequently, when KE is positive. Thus, whether the error voltage is positive or negative, a negative voltage of proportional magnitude will appear across resistor I2! which constitutes an output for this portion of the circuit. The output of the squaring circuit BI is fed by conductor I32 to tube I28 through potentiometer I29 and its associated wiper I3I. Tubes I23 and I 34 serve as a differential D. C. amplifier, as described above for tubes I04 and I05, and have associated therewith common cathode resistor I32 and load resistors I33 and E35. Tube I34 serves as an inverter for the signal by connecting its grid to ground and providing a connection of its cathode with the common cathode resistor I32. The output of tube I28 is then fed through conductor 36 to a cathode follower circuit including tube 31. The output of tube I 34 is fed to a cathode follower circuit including tube I38. Tube I3! has cathode resistors I39 and MI, and cathode follower I38 has associated therewith cathode resistors I42 and I43. These tubes then have a common balancing cathode potentiometer I44 and an adjustable common cathode resistor I45. The outputs of these cathode followers feed rectifiers I45 and I4! in a manner identical with that described above for rectifiers I2! and I 24. These rectifiers are connected to resistors I48, I48 and I5I, and feed a common output resistor I21. Thus, the voltage present across I2! is now proporticnal to IKEIHE I. This potential present across output resistor I 2'! is thence fed by con ductor I52 to the on-off control designated 59 in Fig. 3, which may be any voltage responsive switch device. Thus, when the absolute magnitude of this volta e. which is proportional to a function of the absolute values of error and error-rate, reaches a predetermined magnitude, it actuates the on-ofi. control 59 and applies full torque to the load 34. The switch device 59 emplayed. h re n is ne. h v n l re-e hvsteresis. That is. the magnetic structure is such that the current necessary to ma ntain actuation is much less than that necessary to originally actuate the device. This provides a delay in the reversion of operation to the linear mode upon reaching the torque reversal curve and will allow the phaseplane portrait to a proach the origin while still operating in the full torque mode.

Souar n circuit 9| is illustrated in Fig. 5 and its input-output characteristics are plotted on the curve of Fig. 6. The desired curve 3! is i1lustrated in Fig. 6, whi h would correspond to a true absolute parabola, 631 :3360. where e1 is the input voltage and on is the output voltage of squaring circuit 9|. In comparison therewith is the output 302 of the circuit shown in Fig. 5 showing that in the range within which it is here utilized, the correlation of actual to theoretical values is very close.

The manner in which the squaring circuit operates is as follows: A voltage of volts D. C. is applied to terminal I59 in Fi 5 and thus current flows through resistors IGI, I52, I53, I64, I56, I6 and Hi. store It! and 5'15 are re at v lv lar e com a ed to remaining resistors in this series circuit. Thus, the voltage drop across each of the remaining resistors of the series circuit will be of the order of one or two volts. This will constitute a D. C. bias on each of the triodes I12 through i8I. A eries circuit exists between terminal I83, which is the circuit input, diodes 72 through I 8! in parallel, their associated resistors I34 through I93, the biasing resistors I 52 through IE9, resistor I94, and

"steam around. If a zero voltage is present between terminal i223 and ground, it can be seen that each of the diodes E72 through 285 will be biased by their associated resistors 552 through its in such a manner that no conduction will occur through anyof the biased diodes. As the signal er becomes positive, tube I16 will first begin to conduct through its associated resistor 58%, and as thevoltage e1 continues to increase, successive tubes 575, lid, ill; and H2, which have their plates connected to terminal E83, will also begin to conduct. By the proper choice of resistors ass through use, the conduction through these parallel diodes can be controlled to closely approximate a parabolic relationship. If e1 assumes negative values the term nal E83 is negative with respect to ground, and tubes Ill through l8! will operate in a manner similar to that previously described for tubes H2 through 116. For a small negative value of voltage or, tube I'll will begin to conduct and will cause a voltage to exist across terminals 295 and 59B, and as the negative value of voltage increases, successive tubes H8, I19, Hill and 585 will successively begin to conduct and will pass a current determined by the magnitudes of their associated resistors Hill! to 93. Thus, by the proper choice of biasing resistors 52 through its and current limiting resistors H89 through 593, an input-output voltage relationship is established which very closely approxi mates a parabolic curve as illustrated in Fig. 6.

i illustrates a second embodiment in which the teaching of this invention is used to control the characteristics of a D. C. motor. A rotating shaft 293, which serves as a controlling element, is compared with a rotating shaft 282 which is driven by the output and is the element to be controlled. These are differentially con nected to produce a voltage E proportional to their positional difference or error. This may be accomplished by using potentiometers similar to that shown in. Fig. 3, or any other type of differential device. This error voltage is then fed to an electrical difierential device 2H3 through conductor tilt; and is combined with the output of a tachometer generator 23 to provide an additional voltage proportional to output velocity to provide output damping for the servo. The combined voltage, proportional to error and outb t tY. is then fed to a D. C. amplifier 26?, such as a differential amplifier, through conduc-= tor 285. The double-ended out ut of this D. C. amplifier is then placed upon the grids of two vacuum tubes 2555i and 2% in order to control the current in field coils 2i i and 252 which are a portion of the D. C. source of motive power. The output of the D. C. amplifieris placed on the corn trol grids of tubes 2% and 2539 in a manner to produce increases in iiow of current through tube 2% and field winding 2 ii in direct pro ortion to the signal voltage generated by the differential 2th. The current in tube 2% and its associated field winding 252 is inver ely proportional to the si nal voltage generated by clifierential 2H3. Thus. the windings 2! i and H2 are differentially wound and when. no signal is fed through conductor 2%, the net field flux is substantially zero. Positive or negative signals at 25355 will produce additional flux and the proper positive or negative directional torque compensation. The armature 255 of the driving means of this servo is energized by a voltage source 2%. Voltage source Zifi has in series with it a current limiting resistor 2 ii and a pair of shorting contacts 2:8, 255 in parallel therewith. During the, linear operal2 tion of the servo mechanism, contacts tit and 2 it remain open so that resistor 2i i is in a series circuit with the armature winding 255 and the voltage source Elli. Thus, some torque les than the maximum available from the clrrvin means will be applied during linear op ration. Mechanical gearing means for the load are indicated as Ell, the load schematically as Elli, and output friction as 2 it.

The output of the differential which proportional to the error is also fed 0 a computer which consists of a circuit 225 wnich applies a constant multip r K, a circuit to take a predetermined function of the error which will be substantially a second degree function, connesting means between 22% The output of circuit .222 is to a summation cincuit 22 through a conductor 22%, this sum mation circuit feeds a voltage to boundary control and direction control The output of multiplier is also applied to a difierentiating circuit th' connector 229 to generate a voltage proportional to This voltage is also injected in the summation circuit 22% and. thence the combined voltage proportional to K E+g El is fed to the boundary control and direction control Thus, when the voltae'e output or the summation circuit reaches a value indicates that the function i'i(E+o(E)) cached a predetermined mag- Ly control 225 is en rgized, closing contacts 22. and completing the circuit through contacts 258 and 2% At same time, the direc ion control will have activated either switch 229 or 23!, depending upon the direction of torque requirements of the device and in a like manner will energize either switch 232 or 233, depending upon the torque direction requirements. When this occurs, full voltage, and, consequently, full current is available for the armature Winding i= through contacts 2:8, 2l9 from the voltage source 2H3 as the resistor 25 i has now been shorted out of this circuit. Additional auxiliary field winding 23 or auxiliary field Winding 235 is energized by voltage source 235 or 2? to apply an additional torque to the load in the desired direction. The closin of switch 232 or .233 grounds the grid of either tube E 38 or 2%, and will thus cause the maximum current to flow in the tube having the grounded grid. Thus, when this device is operat ing as a contactor servo, the maximum torque available is increased in three distinct measures;

first by the application of maximum field voltago through the normal field coils 2H and 232; second, by t .e app ication of a substantially increased armature current by the removal of re sistor 287 from the armature circuit; third, by the use of auxiliary field windings or 235. Gbviously, the choice of which h ld winding will be energized at a given instant will be determined by the direction in which it is desired to apply the torque.

Fig. 7 is a schematic representation of the co1nputer circuit of Fig. 6 diagrammatically illustrated by blocks 22%, 222, 22s and 228. This circuit operates as follows: [in error voltage E is applied at terminal 236 which will alter the current in triode 23? which, with tube 238, forms a difierential amplifier. Tubes 23? and 23? have a common cathode resistor 239 and respective load resistors 24! and 262. The load resistors are then connected to potentiometer 2 53, which is connected to a source of D. O. voltage 2%. Potentiometer 263 is used to adjust the load resista-nce of tubes 23! and 2.3.8 inorder to balance out any steady-state differences between tube, which might be present. The gridof. tube 238 is grounded and thus the current in tube 23 is modulated by the cathode, bias across resistor :39. Thus, if a positive voltage is applied to terminal it will cause the cathodes of tubes 23? and to become more positive, producing a negative relative voltage on the grid of, tube 232,-. The output of tube is connected to a secondtriode ass and the output of tube 2% is connected to the grid of tube 25%. The purpose of this circuit arrangement is toJ-cancelany transient changes in voltage or: tube characteristics which are usually detrimental in the. operation oil). C. am plifiers. Tubes Elii and 2% have a common cathoderesistor 24? and tube has plate directly connected to. a regulated l50-voltDl C. supply Tube zee has a load resistor 25% is connected to the 250-volt D. C. supply 2&4, Thus, when a signal is applied to terminal these two stages cfD. C. amplification act inthe usual manner, but in. the event of a change in supply voltage from the source 25%, while con duction would increase in both tubes 23? and 23S causing an increase in output from both of these tubes, the effect on the output of tube 256 would be eiTect-ively cancelled by the efiect of the change in current of tube 245 upon the bias voltage across resistor 24?. The output of tube 246 is proportional to KE, the error voltage times an arbitrary constant, and now fed through a dif ferentiating circuit consisting of condenser 248 and resistor 249; The relative magnitudes of these two circuit elements ar so chosen that the voltage present at point 25E will be proportional to the first derivative KFL or" the voltage KE. This voltage is now applied to the grid of tube 252 which is connectedas a cathode follower havi lg cathode resistor 253 and cathode potentiometer The output of tube 245 is also fed through conductor see, resistors 255 and 256, and potentiometer 251 totriode 2158. Tube, 258 has a cathode resistor 259 and its plate, is directly connected to the loo-volt regulated supply 249 only partially shown here as a regulator tube. The output of tube 258 is taken at its cathode and fed through resistor 26! and network 262 so that the voltage present in conductor 263 will be proportional to the function 903) will be fed to the grid of tube 2%. Network 262 includes semiconductor type rectifier 363 oriented to conduct when the cathode of tube 258 is negative and semi-conductor rectifier 3514 oriented to conduct when said cathode is positive and associated series resistors 3'35 and 355 connected to ground. Rectifiers 3G3 and 3% are chosen for their conduction characteristics in the small current range, which is substantially a souare law relationship. This is to give a computer curve similar to curve it, i l and 16. of Fig. 1. Tube 264 has cathode resistor 25-3 and. potentiometer 254 common with trio-dc 252, and in this manner a summation is taken of KE and 9GB) to produce voltage proportional to-K(E+g(E) This voltage is now applied to the grid of triode 285. Triode 255 has cathode 'esistor 2.55 cormnon with a second triode 2.5]. In this manner, for any signal impressed upon the grid of. 255 a signal of opposite relative polarity is applied to. the grid of tube 2b? which is grounded. Tubes 265' and 26? have load resistors 258 and-2G9 and balancing potentiometer Eli connected therewith, and the wiper of potentiometer 2?! is connected to the 250-volt D. 0. supply 244. Tubes 265. and 2c! operate' asia signal inverter, as. has been described previously. Thus, for a given input to the grid of tube 265, a signal of given polar" is applied to the grid of tube 2'52 from the output of tube 255 and a signal of opposite po a ty is applied to the grid of tube 2'53, represen the output of tube 26?. These tubes Eli? and common cathode resistor 27% and a cathode l icing po tentiomet 1' F5. resistor 2 45 connected to its plate and load r then connected to the 250-volt like manner, the plate or tube a to load resistor 'Z'll which is th supply 254. The out-put of tube to co a. voltage divider co sisting of re.-,is 21'9- and potentiometer 2:35 and t relay control tube 282. Tube directly connected to the voltage has in its cathode circu t resistor F .iustable resist r 255 to it the e coil 283. In alike manner, tube 2 pressed upon, its grid a signal from tub= 3:3 which will always be of opposit polarity to the signal of tube 2l'2. The signal of tube 213 is applied to the grid of tube 2% through a voltage divider consisting of resistors and 223 so that in a zero signal condition, relay coils Z-L-c and will have the some current flowing th 1, and as these coils are differentially associated there would be no resultant force therelrorn. However, for all values of K l+g E other than zero, th (inferential relay uill be actuated. Relay coil 283 and 239 control switch contact 233 and 2 3 of 7 when the current in is the larger and actuates switches 232 and 225 when the current in coil 239 is the larger. Thus, it is seen that tubes 282 and 236 and their associated circuit elements comprise a direction. control for a s cond mode of operation of this servo mocha-n" ing cathode resistor and the output taken across resistor 2553 and. applied to the i. networkcircuit 2%. The grid network 2% acts as a comparator so that no 0 n the input is of a predetermi ed n The magnitude of the variable resistor 2 determines the magnitude of current which must flow in tube 292 before a voltage will appe r on the grid of tube 293. The output of this 9 'cuit then supplied through conductor to tube which it controls relay coil which connected in its plate circuit. Tube 296 has cathode resistor 35% associated therewith, and tube 2 has common cathode connection with tub-e cathode resistor Still. The grid of l grounded. Thus, when the grid of tube becomes positive, the cathode effectively becomes more positive, which. relatr-se negat've voltage to appear upon the grid of Thus, if-the grid of tube assumes relativ positive voltage with respect i cathode, Quillcient current v ill flow in relay the contacts 221, 223 and close conta 298'. 2oz? becomes sufficiently negative, tube w l c. not and also complete the circuits contro led by 22?, 228 and contacts 228 and t ere will'bec range of values of vol tional to K E+cE which will 1103 b actuate to overcome the bias of network ran e the coils will be cle-energid the servo will operate in linear mode. lay coils and 299 and their associated tubes and resistor the servo mechanism here described constitute the boundary control 226 of Fig. 7 so that at any time that the magnitud of the voltages proportional to error and error rate become sufficiently large, one of these relays 2%: or 29% Will be energized and will close switches 22'? and 225 and complete the circuit through contacts 2th and 25 Thus, at any time that the error and error rate reach predetermined magnitudes, V1111 operate in its second or as an off-on device, and the magnitude of the voltages proportional to error and error rate, when considered with respect to their polarities, viii dete min the direction in wh ch torque of motor be applied. coils and see must have sufficient to prevent system from reverting to incur node for a predetermined after he computer output falls below the value determined by network 2%.

Thus, a system of position control is taught whereby a control. element can be positioned in the minimum time for all errors of relatively large magnitude and can be positioned with extreme accuracy for steady--state conditions or when the error or error rate magnitudes are relatively small. It should he understood that any desired function of error can be in the computer portion of this invention and still remain within the scope thereof. he teaching herein can be applied to other closed-cycle control systems using various source of motive power, error generating means and load without departing from the spirit and scope or" this invention.

Thus a system and method of position control is taught which will provide optimum control for both near steady-state and transient conditions. This system overo mes the usual difiioulties of maintaining near steady-state agreement nor mally encountered in the contaetor type of servos, and also eliminates the usual problems encountered linear type of servos which arise from poor response time and consequent poor tracking.

Withou further elaboration, the foregoing will so fully explain the gist of our invention that others may, by applying current snowleclge, readily adapt the same for use under varying conditions of service, without elimine -g certain features, which may properly be said to constitute the essential items of novelty involved, which items are intended to be defined and secured to us by the following claims.

We clair.

1. In a position control system, a controlling element, a control ed element, means for producing an error voltage proportional to a positional difference between the controlling elernent and the controlled element, means for driving said controlled element, linear means for normally energizing said diving m ans as an integro-difierential function of said error voltage, means for generating a voltage proportional to said error voltage, differentiating means for generating voltage proportional to the rate of change of said error voltage, means responsive to said differentiating means for generating a voltage proportional to the square of sairate of change while retaining the sign of said rate of change, summation means to combine said voltage proportional to error voltage and said voltage proportional to the square of the error rate, means responsive to the output of said suminatlon means to control said driving means and to apply the maximum force of said driving means in the direction necessary to reduce to zero said error voltage as indicated by the with bined voltage, means for generating a voltage equal in magnitude to said voltage proportional to error voltage but of absolute means for generating a voltage equal iii-magnitude to said square of error rate voltage but having absolute sign, summation means to combine said absolute values, and switch means responsive to said absolute summation to apply such maximum force of said driving means when said absolute summa tion reaches a redetermined value.

2. In a position control system, a controlling element, a controlled element, means for producing an error voltage proportional to a positional difierence between the controlling element and the controlled element, means for driving said controlled element, linear means for normally energizing said driving means to produce a force proportional to an integro-differential function of said error voltage, multiplier means to produce a voltage proportional to said error voltage, difierentiating means to produce a voltage equal to the rate-of-change of said error voltage, parabolizing means to generate from the output of said difierentiating means a voltage equal to the square of said rate-of-change voltage retaining the sign of said rate-of-change voltage, summation means to combine the outpu voltages of said multiplier means and said. parabolizing means, means for generating a voltage equal to the absolute values of the outputs of said multiplier means and parabolizing means, combining means to add said absolute values, circuit control means controlled by the output of said combining means toapply a voltage to said driving means to produce the maximum force of said driving means when the output of said combining means reaches a predetermined. value and circuit control means actuated by the output of said summation means to determine the direction of said maximum force. I

3. In a position control system having a controlling element, a controlled element, means for producing an error voltage proportional to the positional difference between the controlling element and the controlled element, and means for driving said controlled element, linear means for normally energizing said driving means to pro duce a force proportional to an integro-differen tial function of said error voltage, multiplier means to produce a voltage proportional to said error voltage, difierentiating means to produce a voltage equal to the rate-of-change of said error voltage, parabolizing means to generate from the output of said differentiating means a voltage equal to the square of said rate-of-change volt age retaining the sign of said rate-of-change voltage, summation means to combine the output voltages of said multiplier means and said parao olizing means, means for generating voltages equal to the absolute values of the outputs of said multiplier means and parabolizing means, combining means to add said absolute values, circuit control means controlled by the output of said combining means to apply a voltage to said driving means to produce the maximum force of said driving means when the output of said combini means reaches a predetermined value, and circuit control means actuated by the output of said summation means to determine the direction of said maximum force.

4. In a position control system having a controlling element and a controlled element, electromagnetic means for driving said controlled element, error means for detecting. a positional difference between the controlled element and the controlling element, control means for normally energizing said electromagnetic means as an integro-diiferential function of the output of said error means, computer means to generate a control voltage which is a function of the positional difference, rate-of-change of positional difference, and the acceleration characteristics of the system, and switch means responsive to a predetermined magnitude of said control voltage to cause said electromagnetic means to be energized to produce its maximum force.

5. In a position control system having a controlling element and a controlled element, direct current means for driving said controlled element, error means for detecting a positional difference between the controlled element and the controlling element, control means for normally energizing said direct current means as an integro-differential function of the output of said error means, computer means to generate a control voltage which is a function of the positional difference, rate-of-change of positional difference, and the acceleration characteristics of the system, and switch means responsive to a predetermined magnitude of said control voltage to cause said direct current means to be energized to produce its de 6. In a position control system having a conelement, linear control means for normally energizing the field of said direct current means as a linear integro-differential function of the output of said error means, computer means to generate a control voltage which is a function of the positional difference, the rate-of-ohange of positional difference and the acceleration characteristic of the system, and switch means responsive to a predetermined magnitude of said control voltage to substantially increase the field of said direct current means to produce the maximum design force of said means.

7. In a position control system, a rotatable controlling shaft, a rotatable controlled shaft, direct current means for driving said controlled shaft, error means for detecting a positional difference between said controlled shaft and controlling lincar centre-T. ans for normally energizing the field of said direct current means as an integro-diiferential function of the output of said error means, computer means to generate a control voltage which is a function of the positional difference, the rate-of-change of positional difference, and the acceleration characteristic of the system, and switch means responsive to a predetermined magnitude of said control voltage to substantially increase the field of said direct current means to produce the maximum design torque of said means.

8. in a position control system, a controlling element, a controlled element, direct current electric inductive means for driving said controlled element, error means for detecting a positional difference between said controlled element and controlling element, means for generating an error voltage proportional to said positional difference, control means for normally energizing the field of said direct current electric inductive means wherein said energization is proportional to an integro-differential function of said error voltage, means energized by said error voltage generating means for creating a control voltage proportional to a second integro-diiferential function of said error voltage, and switch means responsive to a predetermined magnitude of said second function of error voltage to substantially increase the field and armature current of said direct current electric inductive means to produce the maximum design torque of said means.

9. In a position control syst m having a controlling element and a controlled element, direct current means having a field and armature Windings for driving said controlled element, error means for detecting a positional difference between the controlled element and the controlling element, control m ans for normally energizing the field of said direct current means as an integro-diiferential function of the output of said error means, resistance means serially connected with the armature winding of said direct current means, computer means to generate a control voltage which is a predetermined function of the positional difference, rate-of-change of positional difference, and acceleration characteristics of the system, and switch means responsive to a predetermined magnitude of control voltage to increase the field of said direct current means to a predetermined maximum and remove said armature resistance from the series circuit.

10. In a position control system having a cont liing element and a controlled element, direct current means having a plurality of field windings and an armature winding for driving said controlled element, error means for detecting a positional difierence between the controlled element and the controlling element, control means for normally energizing one pair of the field windings of said direct current means as an integro-differential function of the output of said error means, resistance means in series circuit with the armature winding of said direct current means, computer means to generate a control voltage which is a predetermined function of the positional difference, rate-of-change of positional difference, and the acceleration characteristics of the system, switch means responsive to a predetermined magnitude of said control voltage to increase the field of said one pair of field windings to a predetermined maximum, energize a second pair of said field windings and remove said armature resistance from the series circuit, and switch means to reverse said field at a predetermined time determined by said computer means to bring said controlled and controlling elements into positional and velocity agreement coincidentally.

11. In a position control system having a controlling element and a controlled element, alternating current means for driving said controlled element, error means for detecting a positional difference between the controlled element and the controlling e-ement, control means for normally energizing said alternating current means as an integro-differential function of the output of said error means, computer means to generate a control voltage which is a function of the positional difference, rate-of-change of positional difference, and the acceleration characteristics of the system, and switch means responsive to a predetermined magnitude of said control voltage to cause said alternating current means to be energized to produce its maximum design force.

12. In a position control system having a controlling element and a controlled element, alternating current means for driving said controlled element, error means for detecting a positional difference between the controlled element and controlling element, linear control means for normally energizing the field of said alternating current means as a linear integro-differential function of the output of said error means, computer means to generate a control voltage which is a function of the positional difference, the rate-L change of positional difference and the acceleration characteristic of the system, and switch means responsive to a predetermined magnitude of said control voltage to substantially increase the field of said alternating current means to produce the maximum design force of said means.

1 3. In a position control system having a controlling element and a controlled element, alternating current means having a plurality of field windings for driving said controlled element, error means for detecting a positional difference between the controlled element and the controlling element, control means for normally energizing one of the field windings of said alternating current means as an integro-differential function of the output of said error means, computer means to generate a control voltage which is a predetermined function of the positional differenoe, rateeof-change of positional difference, and acceleration characteristics of the system, switch means responsive to a predetermined magnitude of; said control voltage to apply a maximum voltage to said one of the field windings in excess of the maximum output of said control means, and switcn means to reverse the phase of said maximum Voltage a determined by said computer means tov produce torque reversal to cause. said po it on l difie c n rate of change of positional difference to approach zero coinciden all 14. in a position control system having a rotatable controlling Shaft and a rotatable controlled shaft, electromagnetic means for driving said controlled shaft, error means for detecting a positional difference. between the controlled shaft 2i); and ntrol i g shaf control means for nor mally energizing said ctrernagn t means s a linear integro-difierential function or the output of said error means, computer means to gencrat control voltages which are a predetermined function of the positional difference, rate-ofchange of positional difierence, and the accelera.- tion characteristics of the system, the first of said functions being a boundary control function represented by the equation and the second of said functions being a torque reversal function represented by the equation DONALD C. MCDONALD. KENNETH C. MATHEWS. ROBERT C. BOE.

References Cited the file of this patent UNITED STATE PATENTS Number Name Date 2,382,380 Isserstedt Sept. 4, 194.5 2,445,289 Cherry July 13, 1948. 2,452,769 Lang Nov. 2,. 19% 2,508,162 Herzwald n May 16;, 1951} 2,588,742 McCallum Mar. 11, 19552 2,588,743 McCallum Man 1.1,. .95.2 2,623,943 Adler V V s Dec. 30, L952. 

